METETÍ, Panama—Five months ago, the Barrios family fled economic calamity in Venezuela along with 7.2 million fellow citizens. In April, they picked up again, this time from the country that had taken them in, Colombia. Unable to get the documentation they needed to legalize their status, Franklin Barrios and Rebeca Herrera joined thousands of other Venezuelans leaving Colombia and trying to make it to the U.S., say migrant advocates and the Venezuelan travelers themselves.

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